create a regular grid of points on a surface, starting to a central point

Hi guys,
I'm trying to create a grid of points lying on a surface, starting to a central point and using two diagonals. Every point has to have the same distance to the nearest (1). I tried to do a script using spheres and their projections on the surface... but it was too large and heavy and I stopped... do you know if there is a better way to do this? thanks so much!!

Stefano